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A Buchholz derivation system for the ordinal analysis of KP + Π3-reflection

Published online by Cambridge University Press:  12 March 2014

Markus Michelbrink
Markus Michelbrink*
Affiliation:
Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, United Kingdom, E-mail: m.michelbrink@swansea.ac.uk
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Abstract

In this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Π3-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis of KP + Π3-Reflection. The method used is an extension of techniques developed by Wilfried Buchholz, namely operator controlled notation systems for RS∞-derivations. Similarly to Buchholz we obtain a characterisation of the provably recursive functions of KP + Π3-Reflection as <-recursive functions where < is the ordering on Rathjen's ordinal notation system . Further we show a conservation result for -sentences.

Keywords

finitary proof theoryordinal analysisimpredicative theories
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1237 - 1283
Copyright
Copyright © Association for Symbolic Logic 2006

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